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To make the pie dough: In a medium bowl, whisk together the flour, and salt.
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Cut in the shortening until it's in lumps the size of small peas.
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Dice the butter into 1/2-inch pieces, and cut into the mixture until you have flakes of butter the size of your fingernail.
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Add the water, two tablespoons at a time, mixing with a fork as you sprinkle the water into the dough
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When the dough is moist enough to hold together when you squeeze it, transfer it to a piece of wax or parchment paper. It's ok if there are some dry spots in the pile. Use a spray bottle of water to lightly spritz these places; that way you'll add just enough water to bring the dough together without creating a wet spot.
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Fold the dough over on itself three or four times to bring it together, then pat it into a disk 3/4-inch thick.
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Roll the disk on its edge, like a wheel, to smooth out the edges. This step will ensure your dough will roll out evenly, without a lot of cracks and splits at the edges later. Wrap in plastic and refrigerate for 30 minutes before rolling.
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Preheat the oven to 400°F. Lightly grease a 9-inch pie pan that's at least 2 inches deep. This will make serving the pie easier after it's baked.
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Roll out the pastry for the pie to a 13-inch circle. Transfer it to the prepared pan, and trim the edges so they overlap the edge by an inch all the way around. Tuck the edges up and under, and crimp as desired.
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Put the lined pie pan in the refrigerator to chill for 10 minutes. This firms up the fat before baking, ensuring a flaky texture and it also allows the gluten to relax, so the crust doesn't shrink as much when it bakes.
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Line the crust with foil or parchment paper, and fill it with pie weights or dried beans. Make sure some of the pie weights (or beans) are nestled up against the sides to keep the crust from slumping down in the pan.
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Prebake the crust for 10 minutes. Remove it from the oven, and gently remove foil or parchment with the weights or beans. Set the crust aside to cool while you prepare the filling. Reduce the oven temperature to 325°F.
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Place the chopped pecans on a baking sheet. Sprinkle them very lightly with salt. When the oven temperature has fallen to 325°F, place the nuts in the oven to toast for 10 to 15 minutes, just until you can smell them. Remove them from the oven and set them aside to cool. Increase the oven temperature to 375°F.
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Prepare the filling: In a medium-sized mixing bowl, beat together the eggs, corn syrups, sugar, butter and vanilla. Stir in the chopped pecans, and pour the mixture into the baked pie shell. Arrange the whole pecans on top.
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Bake the pie for 45 minutes, or until it's puffed and the center seems fairly set. Remove the pie from the oven, and allow it to cool on a rack. As it cools, the center will sink; that's OK.
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Cool completely before slicing; store in the refrigerator. Warm individual slices if you like before serving.
